I've tried /setblock to place a trapdoor with block data from 0 through 15, but none places an open trapdoor.  For block data >= 8, the trapdoor is open for an instant, but then closes.

As a side note, the meaning of the bits within the block data seem to be different from what is on the wiki (i.e. different from the Java edition values).  The bits for open/closed and top/bottom are swapped, and the compass directions satisfy bedrock==3-java.

I tried both the Windows 10 edition and iOS on my iPhone 6.  v. 1.4.3.